All Questions
Tagged with abc or approximate-bayesian-computation
28 questions with no upvoted or accepted answers
3
votes
0
answers
268
views
How to use Approximate Bayesian computation to estimate the parameters of a function?
I am new in bayesian analysis and I want to use Approximate Bayesian computation in order to convert an odd giving to me by a bookmaker to a probability that the event occurs. Here is the Python code ...
- 422
3
votes
1
answer
379
views
Is it possible to do posterior predictive checks when using Random Forest for Bayesian parameter inference?
Random Forest algorithm has been recently proposed for estimating parameter values within the context of Approximate Bayesian Computation (Raynal et al 2017). The idea consists of training regression ...
- 135
2
votes
0
answers
36
views
Estimating parameters for a set of related random variables
Suppose I have some random variables
$$X_i \sim Dist(\theta_i)$$
for $i = 1, ..., n$ where $Dist$ is some known probability distribution family and $\theta_i$ are some parameters which may vary ...
- 203
2
votes
0
answers
37
views
ABC approximation Bias
In Approximate Bayesian Computation, we approximate the (true) likelihood of our model, $f(x_{obs}|\theta)$, with the following integral
$$f_{ABC}(y_{obs}|\theta)=\int K_{h}(x-x_{obs})f(x|\theta)dx $$
...
- 2,286
2
votes
0
answers
70
views
ABC Pseudo Marginal
Suppose, that we have observed data denoted as $y_{obs}$, a likelihood function $l(y|\theta)$ where the parameter $\theta$ follows a prior distribution $\pi(\theta)$.
The posterior in the usual ...
- 2,286
2
votes
0
answers
91
views
Choice of Smoothing Kernel in ABC
In Approximate Bayesian Computation, one approximates an intractable likelihood by convolving it with some smoothing kernel $K$ as
\begin{align}
\ell^{\text{ABC}} ( x | \theta ) = \int \ell ( z | \...
- 1,356
2
votes
0
answers
82
views
distance for abc - nonparametric likelihood
When fitting models using abc, data is simulated using parameters drawn from the prior. The distance between the simulated data and the observed data is calculated, and typically if less than a ...
- 33
2
votes
0
answers
131
views
Approximate bayesian computation: model selection on nested models
For model selection within an ABC framework when the models are nested, say model 1 is equal to model 2 on some subset of the parameter space, is it better to try and do parameter inference or use a ...
- 220
2
votes
0
answers
158
views
Should I trust logistic regression in ABC model selection with more statistics than retained simulations?
I am using multinomial logistic regression to aid model selection in approximate Bayesian computation. However, I just realize at the preferred tolerance, the number of retained simulations is ...
- 21
2
votes
0
answers
112
views
Building artificial state space model from noise-less data
I have a discrete time stochastic process, where at each time the state of the system $X_t$
is given by:
$$
X_t = f_\theta(X_{t-1},\epsilon_t), \; \; \text{for} \; t = 1,\dots,T
$$
and, for example, ...
- 21
1
vote
0
answers
56
views
Temperature scaling a bayesian neural network?
I am trying to calibrate a Bayesian neural network. I have already approximated the posterior density for its weights. In order to make predictions the Bayesian way, I am taking samples from the ...
- 11
1
vote
0
answers
42
views
How to mitigate large sample number for multimodal posteriors in Approximate Bayesian Computation-Sequential Monte Carlo (ABC-SMC)?
I want to do Bayesian inference for a model function for which the likelihood cannot be explicitly computed, which is why I turned to Approximate Bayesian Computation (ABC). In particular, I am using ...
- 11
1
vote
0
answers
44
views
How to solve for an unkown probability distribution within a hierarchical model?
The Problem
Given probability distributions $P(\theta)$ and $P(X)$, and given an inverse function $Y=f^{-1}(X,\theta)$ that returns a unique $Y$. How can one estimate the unkown distribution $P(Y)$ in ...
- 11
1
vote
1
answer
65
views
Rejection ABC: Connection with Rejection Sampling?
I am trying to understand the link between (rejection) ABC and rejection sampling. For example, this paper states:
Approximate Bayesian Computation (ABC, Sisson et al., 2018) is centered
around the ...
- 145
1
vote
0
answers
46
views
Hyperparameter optimisation for approximate Bayesian computation
I have a simulation model with an intractable likelihood function and would like to use approximate Bayesian computation (ABC) to obtain the posterior density for the simulator's parameters.
In ...
- 11
1
vote
0
answers
216
views
Calculating the weights in ABC SMC (2 parameters and more)
Im trying to implement ABC SMC for ODE model which has 2 parameters to estimate. I stopped in the step when calculating the weights as it appear in this answer. My question is should I calculate the ...
- 11
1
vote
0
answers
143
views
ABC SMC: How do weights scale proportionally with number of parameters
Having some problems with the ABC SMC algorithm. I'm trying to implement the methods taken from here: Simulation-based model selection for dynamical systems in systems and population biology
How do ...
- 11
1
vote
0
answers
100
views
Population Monte Carlo Algorithm using L2 Distance Measure/ Likelihood Distribution
I am currently struggling with some concepts of the Population Monte Carlo Framework. Initially, I came across this set of algorithms as I am currently trying to infer parameters from a 7D ...
- 11
1
vote
0
answers
71
views
Using constrained regression model to get closer to the true posterior when doing Approximate Bayesian Computation
I'm using rejection sampling algorithm to generate a reference table ($\theta$,SS). Where $\theta$ are parameter values of model M1 and SS the summary statistics extracted from the pseudo-data ...
- 135
1
vote
0
answers
28
views
What defines a "low" predictive error
Using an Approximate Bayesian Computation (ABC) approach I have estimated a parameter from my observed data.
Now, following this vignette from the R package abc (https://cran.r-project.org/web/...
1
vote
0
answers
203
views
Estimating the posterior predictive distribution post regression adjustment when doing Approximate Bayesian Computation
I'm currently correcting the parameter values of the posterior distribution estimated with Approximate Bayesian Computation. The correction is obtained using a multiple weighted linear regression ...
- 135
1
vote
0
answers
243
views
weight updating scheme in ABC SMC
I am trying to develop some intuition about how weights are updated in ABC PMC. The multiple sources suggest:
$
w_t^{(i)}=\frac{\pi(x_t^{(i)})}{\sum_j^N w_{t-1}^{(j)}K_t(x_{t-1}^{(j)},x_t^{(i)})}
$
...
- 259
0
votes
0
answers
60
views
Difference between Bayesian Information Criteria and Approximate Bayesian Computation as model selection
My question is not very technical and more like a discussion but I will be happy to have a technical input for the comparison b/w BIC and ABC.
I am trying to understand and use the best model ...
- 141
0
votes
0
answers
37
views
Bayesian Coresets
From the paper "Campbell and Broderick (2019), Automated Scalable Bayesian Inference via Hilbert Coresets":
We want to create a Bayesian Coreset which is a small weighted subset of our full ...
- 21
0
votes
0
answers
32
views
Sampling for Approximate Bayesian Computation without Simulation
I am trying to use ABC for a physical black box phenomenon. Both the input space and output space are 3D, and there is a proper distance function for the performance space (CIEL*A*B* ΔE). It is not ...
- 1
0
votes
0
answers
118
views
ABC-SMC, how to obtain summary statistics
I'm using the package pyABC which implements the ABC-SMC algorithm. My model is described by fewer than 10 parameters.
I run the code with $N=50$ particles and stop the process after a maximum run ...
- 4,362
0
votes
0
answers
47
views
The Role of Summary Statistics
I am reading about this algorithm called "ABC" (Approximate Bayesian Computation).
https://cran.r-project.org/web/packages/abc/vignettes/abcvignette.pdf (page 3)
Over here, it makes mention ...
0
votes
0
answers
77
views
Parameter values fall outside the prior range after post-hoc adjustments in the context of Approximate Bayesian Computation?
I'm doing simple rejection sampling within the Approximate Bayesian Computation framework, and I use regression adjustments (i.e., non-parametric multiple linear regression) to get closer to the true ...
- 135